ANDHRA LOYOLA INSTITUTE OF ENGINEERING AND TECHNOLOGY:: VIJAYAWADA
LESSON PLAN
|
Subject : MATHEMATICS-1 |
||
|
Year :
I B-Tech |
Semester
: I |
Branch : COMMON TO ALL |
|
Faculty
: B.RAVI SHANKAR |
Reg :
R19 |
Academic
Year : 2020-21 |
COURSE OBJECTIVES:
In this course the students are
introduced to some basic tools in Mathematics which are useful in modelling and
analyzing physical phenomena involving continuous changes of variables or
parameters. The differential and integral calculus of functions of one or more
variables and functions of several variables taught in this course have
applications across all branches of engineering. This course will also provide
basic training in plotting and visualizing graphs of functions and intuitively
understanding their properties.
COURSE OUTCOMES:
|
1 |
Factual |
CO1 : Ability
to understand and explain concepts of convergence and
mean value theorems |
|
2 |
Conceptual |
CO2:
Student’s gain knowledge on
solving differential equations and its applications to various Engineering
fields. |
|
3 |
Procedural |
CO3A:
Ability to apply the basic
knowledge of differential equations. CO3B : Ability to apply the basic knowledge of Linear
differential equations in electrical systems |
|
4 |
Applied |
CO4: Ability to apply Euler’s theorem for
multivariable function and to find extreme values. CO6: Students are introduced finding areas and volumes using
integrals. |
TEXT BOOKS/ REFERENCE BOOKS:
|
T/R |
BOOK TITLE/AUTHORS/PUBLICATION |
|
T |
B. S.
Grewal, Higher Engineering Mathematics, 43rd Edition, Khanna Publishers. |
|
T |
B. V. Ramana, Higher Engineering
Mathematics, 2007 Edition, Tata Mc. Graw Hill Education. |
|
R |
Erwin Kreyszig, Advanced
Engineering Mathematics, 10th Edition, Wiley-India. |
|
R |
Joel Hass, Christopher
Heil and Maurice D. Weir, Thomas calculus, 14th Edition, Pearson. |
|
R |
Lawrence Turyn, Advanced
Engineering Mathematics, CRC Press, 2013. |
|
R |
Srimantha Pal, S C Bhunia, Engineering
Mathematics, Oxford University Press. |
WEB
SOURCE REFERENCES: (Detailed Topic link)
|
W1 |
|
|
W2 |
|
|
W3 |
UNIT – 1: Sequences, Series and Mean value theorems: [Total Classes
: 16]
Activity:
Activity / Schedule of UNIT-1 :
Pre-Class : Videos, E-books, Web links etc…
In-Class : Explanation on concept, discussion,
Poll, doubts clarification, Demo etc..
Post-Class : Discussion Forum, Review on topic,
Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction to Sequence and
series (revise) |
To
introduce Basic concepts of Sequence and series |
Video Link : https://www.youtube.com/watch?v=cr8pmBLmlL8 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
2. |
Limit of
a sequence |
To Understand the concept of Limit
of a sequence |
Video Link : https://youtu.be/LBSnmanUU2Q Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
. Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
3. |
Types of
sequences – definitions |
To Understand the concept of various
sequences |
Video Link : https://youtu.be/rOmeNK6NqF0 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
. Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
4. |
Geometric
series test – problems |
To Understand the concept of Convergence of geometric series test |
Video Link : https://youtu.be/m7ATbosllvs Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation
(30
Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
. Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
5. |
P-series Test – problems |
To Understand the concept of P-series Test |
Video Link : https://youtu.be/m7ATbosllvs Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
. Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
6. |
Comparison Test – problems |
To Understand the concept of limit Comparison Test |
Video Link : https://youtu.be/YYZmWBYTuhU Text Book : Pdf (e-book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
. Discussion Forum on the topic in
the group Review on the topic Share material on the topic Exercises to solve |
|
7. |
Cauchy’s
integral test – problems |
To Understand the concept of Integral Test |
Video Link : https://youtu.be/vxwlEzfweMs Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
. Discussion Forum on the topic in
the group Review on the topic Share material on the topic Exercises to solve |
|
8. |
D-Alembert’s
ratio test – problems |
Able to solve Examples on Alembert’s
Ratio Test |
Video Link : Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
. Discussion Forum on the topic in
the group Review on the topic Share material on the topic Exercises to solve |
|
9. |
Leibnitz
test – problems |
To Understand the concept of Leibnitz test |
Video Link : https://youtu.be/oG6YoERagXM Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
. Discussion Forum on the topic in
the group Review on the topic Share material on the topic Quiz |
|
10. |
Absolute
convergence – problems |
To Understand the concept of Absolute
convergence |
Video Link : Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
. Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
11. |
Conditional
convergence – problems |
To Understand the concept of Conditional
convergence |
Video Link : https://youtu.be/3J3NBe5kiV0 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
. Discussion Forum on the topic in
the group Review on the topic Share material on the topic Quiz |
|
12. |
Rolle’s
theorem - problems |
To understand the concept of Mean
Value Theorem |
Video Link : https://nptel.ac.in/courses/111/105/111105121/ Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
. Discussion Forum on the topic in
the group Review on the topic Share material on the topic Assignment - 1 |
|
13 |
Lagranges theorem – problems |
To understand the concept of Lagranges theorem |
Video Link : https://nptel.ac.in/courses/111/105/111105121/ Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
14 |
Cauchy’s mean value theorem –
problems |
To understand the concept of Cauchy’s mean value theorem |
Video Link : https://nptel.ac.in/courses/111/105/111105121/ Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
15 |
Taylor’s series with Remainder
terms – problems |
To understand the concept of Taylor’s series with Remainder terms |
Video Link : Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
16 |
McLaren’s series with Remainder
terms – problems |
To understand the concept of McLaren’s series with Remainder terms |
Refer the previous Links of all
the concepts in unit-1 |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion or Poll activity (5 min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic Assignment-1 |
UNIT – 2
: Differential equations of first order and
first degree [Total
Classes : 13]
Activity:
|
1 |
Factual |
Reading Prerequisite
concepts- Ordinary Differential Equations and Basic definitions, Videos related to Ordinary Differential Equations, Referring the content on the Internet |
|
2 |
Conceptual |
Video Lectures related to Ordinary Differential Equations NPTEL
Videos Links from the Internet |
|
3 |
Procedural |
Refer to text book content and Understanding the Ordinary Differential Equations with
examples(simple to complex) |
|
4 |
Applied |
Problems
Solving and Applications solving by practice sessions and Assignments Quiz
etc… |
Activity / Schedule of UNIT-2 :
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion,
Poll, doubts clarification, Demo etc..
Post-Class: Discussion Forum, Review on topic,
Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction on Ordinary
differential equations |
To
introduce The concept of Ordinary
differential equations |
Video Link : https://youtu.be/ClvFwUpi3ZA Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion (5 min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
2. |
Introduction to Linear differential equations –
problems |
To
enhance the understanding of The concept of Linear differential
equations |
Video Link : https://www.youtube.com/watch?v=QC3z-NUkOcE&list=PLociSetSILauNfkJkU0PzbFyBHohCI0rT&index=9 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Revise previous class – (5 Mins) Asking Questions on previous class
randomly (5 Mins) PPT
presentation/ class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
3. |
Bernoulli’s differential equations
– problems |
To
understand the concept of Bernoulli’s
differential equations |
Video Link : https://www.youtube.com/watch?v=QC3z-NUkOcE&list=PLociSetSILauNfkJkU0PzbFyBHohCI0rT&index=9 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
4. |
Exact differential equations –
problems |
To
understand the concept of Exact
differential equations |
Video Link : https://www.youtube.com/watch?v=0CNoNmMdBuE&list=PLociSetSILauNfkJkU0PzbFyBHohCI0rT&index=4 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation/ class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
5. |
Non-Exact Differential equations
Type-I,II |
To
understand the concept of Non-Exact
Differential equations Type-I,II |
Video Link : https://www.youtube.com/watch?v=dtbLHtoh_M0&list=PLociSetSILauNfkJkU0PzbFyBHohCI0rT&index=6 https://www.youtube.com/watch?v=Bk9sT1BStlo&list=PLociSetSILauNfkJkU0PzbFyBHohCI0rT&index=8 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
6. |
Non-Exact Differential equations
Type-III,IV,V |
To
understand the concept of Non-Exact
Differential equations Type-III,IV,V |
Video Link : https://www.youtube.com/watch?v=SxYI7EzLVDA&list=PLociSetSILauNfkJkU0PzbFyBHohCI0rT&index=7 https://www.youtube.com/watch?v=Bk9sT1BStlo&list=PLociSetSILauNfkJkU0PzbFyBHohCI0rT&index=8 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
7. |
Newton’s law of cooling - problems |
To
understand the concept of Newton’s
law of cooling |
Video Link : https://www.youtube.com/watch?v=DqFdy6Ad5mg Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
8. |
Natural law of growth – problems |
To
understand the concept of Natural
law of growth |
Video Link : https://www.youtube.com/watch?v=tj993BDRAhU Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
9. |
Natural law of decay – problems |
To
understand the concept of Natural
law of decay |
Video Link : https://www.youtube.com/watch?v=tj993BDRAhU Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
10. |
RL & RC circuits - problems |
To
understand the concept of RL
& RC circuits |
Video Link : https://www.youtube.com/watch?v=5AFJsTYPVo0
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo of cluster configuration(30
min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic configure. |
|
11. |
Orthogonal Trajectories –
Cartesian form – problems |
To
understand the concept of Orthogonal
Trajectories – Cartesian form |
Video Link : https://www.youtube.com/watch?v=NV9nX1a0qoU
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
12. |
Polar form, self orthogonal –
problems |
To
understand the concept of Polar
form, self orthogonals |
Video Link : https://www.youtube.com/watch?v=YfnIRG4HAKE
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/108/111108081/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic Assignment-2 Quiz - 2 |
UNIT – 3: Linear differential equations of higher order [Total Classes:
11]
Activity:
Activity / Schedule of UNIT-3:
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion,
doubts clarification etc..
Post-Class: Discussion Forum, Review on topic,
Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction on Higher order
linear differential equations |
To
introduce The concept of Higher order linear
differential equations |
Video Link : https://www.youtube.com/watch?v=L7Yy0IMshbE
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107098/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion (5 min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
2. |
Solution of homogeneous liner
differential equation |
To
introduce The concept of Solution of
homogeneous liner differential equation |
Video Link : https://www.youtube.com/watch?v=A1KyaRjfnmk
https://www.youtube.com/watch?v=W4GlSFNm2N4 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Pdf : https://hci.stanford.edu/courses/cs448g/a2/files/map_reduce_tutorial.pdf Web Link : https://nptel.ac.in/courses/111/107/111107098/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
3. |
When Q(x) = |
To
introduce The concept of When Q(x) = |
Video Link : https://www.youtube.com/watch?v=q2OVz0z6xa4
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Pdf : https://hci.stanford.edu/courses/cs448g/a2/files/map_reduce_tutorial.pdf Web Link : https://nptel.ac.in/courses/111/107/111107098/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
4. |
When Q(x) = |
To
introduce the concept of When Q(x) = |
Video Link : https://www.youtube.com/watch?v=eQ40pAW3z-0
https://www.youtube.com/watch?v=SiJFc1IuWus
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107098/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
5. |
When Q(x) = |
To
introduce the concept of When Q(x) = |
Video Link : https://www.youtube.com/watch?v=R0qXI6dl1Zo
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107098/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
6. |
When Q(x) = |
To demonstrate
Basic When Q(x) = |
Video Link : https://www.youtube.com/watch?v=3LQAaAh4wM8 https://www.youtube.com/watch?v=jRFIrkdnoMQ&list=PLhSp9OSVmeyLTuT8bf-DZIffkRLmXmLzN&index=9 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107098/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
7. |
When Q(x) = |
To demonstrate
Basic When Q(x) = |
Video Link : https://www.youtube.com/watch?v=NFxs1qqOHaQ
https://www.youtube.com/watch?v=jRFIrkdnoMQ&list=PLhSp9OSVmeyLTuT8bf-DZIffkRLmXmLzN&index=9 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107098/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
8. |
When Q(x) = |
To demonstrate
When Q(x) = |
Video Link : https://www.youtube.com/watch?v=NFxs1qqOHaQ
https://www.youtube.com/watch?v=jRFIrkdnoMQ&list=PLhSp9OSVmeyLTuT8bf-DZIffkRLmXmLzN&index=9 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107098/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
9. |
Method of variation of parameters
– problems |
To demonstrate
Method of variation of parameters |
Video Link : https://www.youtube.com/watch?v=45S-4tR6zCk
https://www.youtube.com/watch?v=jiQ2sX5wGwM Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107098/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
10. |
LCR-Circuits – problems |
To Introduce the concept of LCR-Circuits |
Video Link : https://www.youtube.com/watch?v=MfMiqMOu254
https://www.youtube.com/watch?v=MPAk-R16fLY Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107098/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
11. |
Simple Harmonic motion - problems |
To Introduce
the concept of Simple Harmonic motion |
Video Link : https://www.youtube.com/watch?v=V9bl02Ffo_o
https://www.youtube.com/watch?v=4Jezsfam3w4
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107098/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
12. |
Revision of all the concepts in
Unit-3 |
Revising
all the concepts |
Refer above Links for data |
Revising the concepts discussed so
far Any topic to Repeat asked by
students. |
Assignment-3 Quiz-3 |
UNIT – 4: Partial differentiation [Total
Classes: 10]
Activity:
|
1 |
Factual |
Reading Prerequisite concepts- partial differentiation Videos Referring the content on the Internet |
|
2 |
Conceptual |
Video Lectures On partial differentiation NPTEL Videos Links from the Internet Solved Examples from Internet |
|
3 |
Procedural |
Refer to text book content and Examples, Understanding the partial differentiation with examples(simple to complex) |
|
4 |
Applied |
Problems Solving and Applications solving by practice sessions and Assignments Quiz
etc… |
Activity / Schedule of UNIT-4 :
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion,
Poll, doubts clarification etc..
Post-Class: Discussion Forum, Review on topic,
Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction to partial differentiation |
To
introduce The concept of the partial differentiation |
Video Link : https://www.youtube.com/watch?v=OK88BFOKqQA https://www.youtube.com/watch?v=eTp5wq-cSXY Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://www.sanfoundry.com/engineering-mathematics-questions-answers-partial-differentiation-1/ https://nptel.ac.in/courses/111/107/111107108/ |
Discussion on pre-requisites (5 Min) PPT
presentation (30 Min) Discussion (5 min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
2. |
Taylors theorem – problems |
To Introduce
the concept of Taylors theorem for functions of
several variables |
Video Link : https://www.youtube.com/watch?v=oqjgn2XN3Dc Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107108/
|
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
3. |
Mc Lauren’s theorem - problems |
To
Introduce the concept of Mc Lauren’s theorem |
Video Link : https://www.youtube.com/watch?v=pjv0HtkhifQ
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107108/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
4. |
Jacobian, functional dependent and
independent |
To
Introduce the concept of Jacobian, functional dependent and
independent |
Video Link : https://www.youtube.com/watch?v=xv8WKIrv5WU
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107108/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
5. |
Functional relation – problems |
To
Introduce the concept of Functional relation |
Video Link : https://www.youtube.com/watch?v=oP7RgpIO2Fw
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107108/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
6. |
Chain – rule problems |
To
Introduce the concept of Chain – rule problems |
Video Link : https://www.youtube.com/watch?v=Fbsm7Y-Iav8
Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107108/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
7. |
Maxima and Minima (without
constraint) - problems |
To
Introduce the concept of Maxima and Minima (without
constraint) |
Video Link : https://www.youtube.com/watch?v=N_CyeSqqYs4 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107108/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
8. |
Maxima and Minima (with constraint)
– problems |
To
Introduce the concept of Maxima and Minima (with
constraint) |
Video Link : https://www.youtube.com/watch?v=2bKosTC_YQU Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/107/111107108/ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
9. |
Lagrange method of Undetermined
multipliers-problems |
To
Introduce the concept of Lagrange method of Undetermined
multipliers-problems |
Video Link : https://www.youtube.com/watch?v=N_CyeSqqYs4
https://www.youtube.com/watch?v=7f7q2jdFbcU Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://app.writable.com/explore/writable?type=Collection&grades=Elementary&genres=_ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
10. |
Euler’s Theorem - problems |
To
Introduce the concept of Euler’s Theorem - problems |
Video Link : https://www.youtube.com/results?search_query=+Euler%E2%80%99s+Theorem+-+problems+engineering+mathematics
https://www.youtube.com/watch?v=BzYrhvmlP34 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://app.writable.com/explore/writable?type=Collection&grades=Elementary&genres=_ |
Revise previous class – (5 mins) Asking Questions on previous class
randomely (5 Mins) PPT
presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic Assignment-4 Quiz – 4 |
UNIT – 5: Multiple integrals
[Total Classes : 10]
Activity:
|
1 |
Factual |
Reading Prerequisite concepts- line integral, Double
integral Videos Referring the content on the Internet |
|
2 |
Conceptual |
Video Lectures On line integral, Double integral, Triple
integral Videos and NPTEL Videos Links from the Internet Solved Problems, Examples from Internet |
|
3 |
Procedural |
Refer to text book content and Examples, Understanding the
multiple integrals with examples(simple to complex) |
|
4 |
Applied |
Problems Solving and Applications solving by practice sessions and Assignments Quiz
etc… |
Activity / Schedule of UNIT- 5:
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion,
Poll, doubts clarification etc..
Post-Class: Discussion Forum, Review on topic,
Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction to line,surface,volume
integrals |
To
introduce The concept of line,surface,volume
integrals |
Video Link : https://www.youtube.com/watch?v=NyG0vRn5FfU
https://www.youtube.com/watch?v=JiQW1TQ5MMs https://www.youtube.com/watch?v=hG7h2g36jrQ Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/104/111104085/ |
Discussion on pre-requisites (10 Min) PPT presentation/Class/demo (35 Min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
2. |
Evaluation
of Double integrals – problems |
To
introduce The concept of Double
integrals |
Video Link : https://www.youtube.com/watch?v=XX5-ZgFC85E https://www.youtube.com/watch?v=aqu6v4vdfd4 Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/104/111104085/ |
Discussion on pre-requisites (10 Min) PPT presentation/Class/demo (35 Min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
3. |
Change the order of integration –
problems |
To
introduce The concept of Change the order of
integration |
Video Link : https://www.youtube.com/watch?v=QbkiHZfGdZU
https://www.youtube.com/channel/UCFp0mDTHxb4kmzYEI7idxOQ Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/104/111104085/ |
Discussion on pre-requisites (10 Min) PPT presentation/Class/demo (35 Min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
4. |
Changing
in to polar co-ordinates – problems |
To
introduce The concept of Changing
in to polar co-ordinates |
Video Link : https://www.youtube.com/watch?v=oPLMH4q3kNk
https://www.youtube.com/watch?v=TKM3MF2m7vU Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/104/111104085/ |
Discussion on pre-requisites (10 Min) PPT presentation/Class/demo (35 Min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
5. |
Changing
of variables – problems |
To
introduce The concept of Changing
of variables |
Video Link : https://www.youtube.com/watch?v=1MoIt6vC0gU
https://www.youtube.com/watch?v=3hyciaX4cSQ Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/104/111104085/ |
Discussion on pre-requisites (10 Min) PPT presentation/Class/demo (35 Min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
6. |
Volume
integrals – Evaluation |
To
introduce The concept of Evaluating Volume integrals |
Video Link : https://www.youtube.com/watch?v=hG7h2g36jrQ
https://www.youtube.com/watch?v=g89jZhB1X3s Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/104/111104085/ |
Discussion on pre-requisites (10 Min) PPT presentation/Class/demo (35 Min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
7. |
Mass of
triple integrals – problems |
To
introduce The concept of Evaluating Mass of triple integrals |
Video Link : https://www.youtube.com/watch?v=yqstdcWdHDs https://www.youtube.com/watch?v=Fm63pdzBl1o Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/104/111104085/ |
Discussion on pre-requisites (10 Min) PPT presentation/Class/demo (35 Min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
8. |
Mass of
triple integrals – problems |
To
introduce The concept of Checking out the Pig Script
Interfaces |
Video Link : https://www.youtube.com/watch?v=yqstdcWdHDs https://www.youtube.com/watch?v=Fm63pdzBl1o Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/104/111104085/ |
Discussion on pre-requisites (10 Min) PPT presentation/Class/demo (35 Min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
9. |
Volume
of cylindrical co-ordinates – problems |
To
introduce The concept of Volume of cylindrical co-ordinates |
Video Link : https://www.youtube.com/watch?v=cghy5cEoCNg
https://www.youtube.com/watch?v=vjYPfdKPJJM Text Book : Pdf (e-book) CANVAS
INSTRUCTURE Web Link : https://nptel.ac.in/courses/111/104/111104085/ |
Discussion on pre-requisites (10 Min) PPT presentation/Class/demo (35 Min) Summary (5min) Doubts clari-fication (10 min) |
Discussion Forum on the topic in
the group Review on the topic Share material on the topic |
|
10. |
Revision of all the concepts in
Unit-5 |
Revising
all the concepts |
Refer above Links for data |
Revising the concepts discussed so
far Any topic to Repeat asked by
students. |
Assignment-5 Quiz-5 |
TOTAL CLASSES: 60
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